This assumption will enable us to treat, in
the GSP framework, every \(Z_j\)  as an
analogue of the ISP metric \(\Theta \)  of
Eq. (REF ).
This means that
every such an operator will have to satisfy the
consistency conditions as listed, e.g.,
in Eq. Nr. (2.1) of
the physics-oriented review [1]}.
These mathematical
conditions involve the domain-completeness (cf. Nr. (2.1a)),
Hermiticity (2.1b) (equivalent to
our present
Eq. (REF )),
positive definiteness (2.1c)
and the metric-boundedness constraint
Nr. (2.1d) plus, let us add, the metric-inverse boundedness constraint
missing in [1]}.
Still, the authors of
review [1]} formulated a consistent theory because they managed to
circumvent certain formal difficulties
as mentioned by Dieudonné [4]} by restricting their
attention, drastically, just to the not too realistic models
possessing bounded-operator Hamiltonians. In contrast, Dieudonné
himself revealed that once the class of Hamiltonians
remains sufficiently general, the ISP metric \(\Theta \)  need not exist
at all.
